Timbre control for string instruments



Jan. 15, 1963 c. R. EVANS TIMBRE CONTROL FOR STRING INSTRUMENTS Filed Nov. 18, 1959 INVENTOR Mia/wry flwvfiafw ATTORNEXS United. States Patent 3,073,202 TIMBRE CGNTROL FORSTRING INS'IIRUMENTS Chauncey Richard Evans, Salt Lake City, :Utah, assignor to Star Valiey Electronics, lnc saltLake City, Utah, a corporation of Utah- Filed Nov. 18, 1959,Ser.No. 853,832 7 Claims. (0]. 84-L14) mentalfrequency also may be produced, each representing the resonant frequency of a fractional partofthe'total vibrating lengthofthe string. :The second'harmonic 'is two'timesthe fundamental frequency,-the.-third harmonic is threetimes the fundamentalfrequeucy,-etc.

.Thisnpatterngis'characteristioof all vibrating strings in musical instruments. Yet it is well known that two strings having the same fundamental frequency'may 'pro duce different tones. For example, it is easy to distinguish between tones of the same fundmental frequency pro- ;duced-bya piano andby a violin.

'The quality by which two tones of "the same fundamental frequency orgpitchmayvbe distinguished' from. each other is called 'timbre. {It .depends 'in' large measure upon the relative emphasis given tothe various harmonics. A string is capable of-being vibrated in many different patterns, and, each pattern produces a distinctive tone quality.

Over the centuries, various techniques for affecting timbre :have been used by'makers .of .stringrinstruments and by the musicians who play the instruments. :The

nature of the stringritself audits mounting are factors of importance in determining the mode of vibration-of the string. Themethod by which the'string isset in motion also maybe important :as far as the resulting toneis concerned, and various techniques, such as bowing,harnmering, and plucking, have been utilized to obtain different elfects. Similarly,theplacealongthellength of thestring Where it is contacted by the actuating means is significant, becausethestn'ngis incapable of vibrating at'a frequency which would produce a-nodeat the exact-point of actuation.

lttisan object of the;present;invention to provide'st-ill other meansv for and-methods of'con'trolling the timbre :of musical tones derived from vibrating strings.

A more specific object of the invention is to provide a system lay-which selected harmonics developed in avibratthatincludeonlythe odd-numbered, or only the evennumbered "harmonics generated by the vibrating string. :Thefo'regoing objects may be-realize'd, according to a preferred :embodiment of the invention, by providing an instrumentin-Which a piezoelectric transducerisdisposed incontact with each endof the vibratinglength of a string and in which the electricahoutputsfrorn jthetwo transducersare-selectively combined-and then utilized to drive a'loudspeaker system. The-mannerin which'thefsignals phase will cancel.

3,073,202 Hatented Jan. 15, 1963 from the two transducersare combined will determine the .relative intensity. oftheodd. andeven-numbered harmonics pull-amend of the string awayfrom its support willdiminish the pressure of that end against its support. Conversely, any component which tends ;.to;press an end of thestring toward its support will increase thepressure of that end against the support. When piezoelectric transdueers are associated with the support means, they'will respond to these pressure variations, and, each=transducer Will produce electrical signals having frequencies corresponding to the frequencies appearing on the vibrating :s in

It is necessary at this point to give specific, consideration :to the phaserelationships of the pressure variations at the two ends of the vibrating-lengthpf a; string. In order to simplify the discussion, ;it will be assumed that the ,stretched string is mounted so as to bear downwardly against-supports at each end; of its vibrating length.

In producing its fundamental --frequency, or first harmonic, the whole vibrating lengthrof the string moves as a unit. Therefore, the pressure variations atthe two ends of-the string resulting fronr this component of vibratory motionof the string will be exactly ,in ,phase .with each other. Whenever thepressure at one end increases, the pressure at the other end, also increases. A different effect is produced ,by thesecond harmonic. This componentof the vibrating motionofgthe string results from resonant vibrations ofeach of the two halves of thelength of the string, andthe vibrationsofone half are one hundred ,and eighty degrees out of phase .with the :vibrations 'of the other half. When one half is moving upwardly, the other half is moving downwardly. Thus, the-pressure variationsatthe endsupports for the string will .beone hundred and. eighty degrees out of phase.

The higher harmonics followthepattern; of the first. and second harmonics. The pressure variations at the .end supports due .to the odd-numberedtharmonics,-i;e., thefirst,

degrees out of phase.

Since the electrical signals from.thepiezoelectric transducers are functions ofthe pressure variations developed at the ends of the vibrating string, they will follow this same pattern as far-asphase is-concerned. The output signals from the two transducers resulting .from oddnumbered harmonics developed in the string will hear :one phase relationship to each other, while signals resulting from even-numbered harmonics will bear an opposite phase relationship.

The present invention I provides .forcombining the electrical signalsfrom the .two transducers in such a vWay that selected harmonics are cancelled v.or eliminated. 'For example, when the positive terminal ,of one transducer is coupled tothe positive terminal of the other transducer and .themegative terminal ofonetiscoupled to the negative terminal of the other the signal com .ponents thatare one hundred and eighty degrees .out Of Only these signal components that are in phase will ;be .permitted to' pass to the loudspeaker system for conversion into acoustic energy. Conversely, if the transducersareconnected so that th e positive terminalrof each is coupled .to the negativegterminal of the other, only .out-of phase signal eomp onents will :be available for the productions pfsound.

The coupling system for the transducer outputs also may permit selective alteration of the relative magnitudes of the transducer signals so as to effect partial cancellation of certain signal components. In this way, it is feasible to control the degrees of cancellation and thereby to control the relative emphasis of the odd and even harmonics in the tone.

Thus, the tone created when the string is vibrated may be a tone from which all of the even-numbered harmonies or all of the odd-numbered harmonics have been removed either wholly or partially. This gives a Whole new dimension to the field of timbre control. By utilizing the principles of this invention, it is possible to construct musical instruments capable of producing many novel tone effects.

A more complete understanding of the invention will be gained from a consideration of the following description of certain embodiments illustrated in the accompanying drawings, in which:

FIG. 1 is a diagrammatic illustration of a string instrument constructed in accordance with the invention;

FIG. 2 is a chart depicting the first few mode of vibration of a string;

FIG. 3 is a circuit diagram illustrating the manner in which the signals derived from a string of the instrument may be combined and converted into sound energy; and

FIG. 4 is a diagram of another circuit for combining the signals derived from the string.

In order to simplify the disclosure of the invention, a very simple string instrument has been chosen for illustration in FIG. 1. It includes a single string 12 stretched between a pair of mounting pins 14 carried by an elongated support 16. Also mounted on the support 16 are two bridge structures 18 and 20 which bear against the stretched string 12 and actually define the terminals of the vibrating length of the string 12.

It will be understood, of course, that the invention is not limited to the elementary instrument 10. It may be utilized in instruments having many strings, and it may be combined with other timbre control techniques in various ways.

The bridge structure 18 includes a ceramic piezoelectric body 22, and the bridge structure 20 includes a ceramic piezoelectric body 24. The piezoelectric bodies 22 and 24 serve as transducers. They are arranged so as to respond to the vibrations of the string 12 and they convert the mechanical energy firom the string 2 into electric energy. The transducers 22 and 24 respond to the pressure conditions which exist at the very ends of the vibrating length of the string 12. Other type of transducers capable of responding to the string 12 only at locations where the string 12 moves through substant-ial distances are not suitable.

It will be assumed in this description that the transducers 22 and 24 are matched in the sense that they will produce equal electrical signals in response to equal inputs of mechanical energy. However, this condition is not of critical importance, and it will be evident that unmatched transducers may be employed without departing from the principles of the invention.

Since the transducers 22 and 24 respond to the conditions at the ends of the vibrating length of the string 12, it will be desirable at this point to consider briefly the nature of the efiects produced at the ends of the vibrating string. The first five harmonics for a string S are depicted in FIG. 2 in a conventionalized form. In this view, the ends of the string S are represented by the dots located at the intersections of vertical lines A and B with the horizontal lines representing the axis of the string S.

The first harmonic for the string S is its fundamental resonant frequency. In producing this frequency, the string S vibrates as a unit. Hence, the string S always pulls both of its ends in the same direction relative to 4 the horizontal axis of the vibrating string S. In FIG. 2, this condition is represented by the small arrows near the ends of the string S, and it will be observed that, for the first harmonic, both of these arrows point in a direction having an upward component.

The second harmonic for the string S is an exact multiple of the first harmonic. In order to produce this frequency, half lengths of the string S become the vibrating units, with a node being disposed midway along the length of the string S. Note also that the two half lengths of the string S are one hundred and eighty degrees out of phase with each other. The arrows show that when one end of the string S is being pulled upwardly, the opposite end is being pulled downwardly.

The third harmonic requires that three equal segments of the string S be vibrated as units, with two nodes being disposed intermediate the ends of the string. Again, however, adjacent segments will be one hundred and eighty degrees out of phase with each other. The result is that the two end segments will always be in phase with each other. Both ends of the string S pull in the same direction, as shown by the arrows.

The fourth harmonic is similar to the second harmonic in that its end portions must always be one hundred and eighty degrees out of phase with each other. The fifth harmonic is similar to the first and third harmonics in that its end portions must always be in phase with each other. Higher harmonics preserve this pattern. For all even-numbered harmonics, the end portions of the string S will be one hundred and eighty degrees out of phase. For all odd-numbered harmonics, the end portions of the string S will be in phase.

Since the transducers 22 and 24 respond to the conditions which exist at the ends of the string 12, it will be evident that the electrical signals produced by these transducers will follow the phase pattern suggested in FIG. 2. When the string 12 is vibrated, that component of its vibratory motion that results in the production of the first harmonic .will cause pressure variations in the transducers 22 and 24, and these variations will be in phase with each other. In fact, the pressure variations resulting from all of the odd-numbered harmonics will be in phase. Whenever the pressure on one transducer is increasing, the pressure on the other will be increasing simultaneously, and

vice versa.

The components for vibratory motion that produce the even-numbered harmonics will be reflected by out-ofphase pressure variations upon the transducers 22 and 24. When the pressure in one is increasing, the pressure in the other will be decreasing.

This distinctive phase pattern permits the signals from the transducers 22 and 24 to be combined in such a way as to cancel out selected groups of harmonics. The circuit depicted in FIG. 3 illustrates this concept. 1

This circuit includes switch means 26 having four contacts 23, 3t 32 and 34, and two blades 36 and 38. The blades 36 and 38 are mounted so that they may be moved simultaneously. In one position of the blades 36 and 38, the blade 36 cooperates with contact 28 and the blade 38 cooperates with the contact 30. In another position of the blades 36 and 38, the blade 36 cooperates with the contact 34, and the blade 38 cooperates with the contact 32. It is desirable also that the blades 36 and 38 be mounted so that they may be positioned between adjacent pairs of the contacts 28, 30, 32 and 34.

The piezoelectric transducer 22 is connected to the contacts of the switch 26. Its positive terminal is connected to the contacts designated 28 and 32, while its negative terminal is connected to the contacts designated by the numerals 30 and 34. The blades 36 and 38 of the switch 26 are connected respectively to the negative and positive terminals of the other transducer 24 by leads 30 and 42. It is preferred that the switch blades 36 and 38 be mechanically connected together for simultaneous movement, as suggested by the broken line in FIG. 3.

so e-26a Thesignal appearing across the leads 40zand 142 is fed to a conventionalamplifier 44, and theamplified signal drives a conventional loudspeaker system 46. These components are well-known'in theart, and theyneed not be described in detail here. 7

When the switch means 2,6.is in thecondition shown infull lines in FIG. 3, thepositive terminal of thetransducer 22 is coupled-to the negativeterminalof the transducer;24, andthe negative terminalot thetransducer 22 is coupled to the positive terminal of .the transducer 24. The result producedbythe circuitwhen the switch means is in this conditionis a cancellation of all odd-numbered harmonics generated by the vibrating string 12.

This result can be understood vby again referring to FIG. 2. For t-he-odd-numbered harmonics,,the pressure variations at the two ends of the vibrating length of the stringalways are'inphase with each other. Thus, whenever one ,of'these odd-numberedharmonics causes the voltage of the positive terminal of one of the transducers to increase, it also will fcausethe voltage of the positive terminal of theothertransducer .tojincrease simultaneously. At the same time, the voltages at .the'negativeter- .minals of bothofthetransducers 22 and'24 resulting from these odd-numbered harmonics will be decreasing. Therefore, if .the v positive terminal of one transducer is coupled to the.negative terminal of the other transducer, cancellationof the odd-numbered iharmonics' will occur.

The only signals remaining on the leads 40 and 42 will' be thosederived from t-he 'even-numbered'harmonics generated'by the vibrating string 12. These signals will pass to the amplifier 44, and then they will serve to drivethe loudspeaker system 46 to "produce atonehaving distinctive qualities.

.In this connection, it should benoted that a tone from which the fundamental resonant frequency'has been eliminated cannot be produced by conventional string instruments. The fundamental isalwayspresent when a string is vibrated.

When the switch means 26 is conditioned-so that its blades 36 and 38 are connected electrically to the contacts.32 and '34, the signals from the transducers 22 and 24are combined in an opposite manner. The positive terminals of the ,twotransducers will be connected together, 'andthe negative terminals of the two transducers willbeconnectedtogether. -As-a'result, those harmonics that areout of phase at the ends of the vibrating length of the string 12 will be cancelled. These are the evennumbered harmonics, as suggested in FIG. 2. 'Theoddnumberedharmonics will pass to the amplifier 44 and to the speaker '46 for conversion 'into sound.

The third conditionof the-switch means '26 is onein which the blades 36--and 38do not abutagainst anyof the contacts 28,30, 32 and 34. When'the switch means :is in this position, the transducer 24 is coupled directly to the amplifier 44, and the amplifier will receiverall of the harmonics generated in the transducer 24in response to the vibrations of the string 12. The tone emanating from the loundspea'ker system 46 also will include all the harmonics.

It will be'observed'thattheswitch26in FIG, 3 provides for complete cancellation of certain groups of harmonics.

That is to sayythe out-of-phasesignals are of equal magnitude, so that when they are combined, a null results.

However, the inventionis not limited to complete cancellation, and "FIG. 4rillustrates-an embodiment in which partial ca'ncellationmay be achieved When desired.

In the embodiment of FIG. 4, the signals from the transducers 22 and 24 are combined in a voltage divider network 48. Two resistors '50 and 52 are connected in parallel across the positive and. negative terminals of the transducer 22. The positive and negative terminals of the transducer 24 are connected through the leads 40 and 42 to contacts 54 and 56 that are movable along the resistors 50 and 52. It is preferred that the contacts 54. and 56 be mechanically coupled together, as indicated by the broken line-in FIG. 4, so as to move simultaneously tinopposite directions along'their respective coils.

It will be observed that the voltage at the left end of each of the resistors and 52 will conform to the voltage at the negative terminal of the transducer 22. Similarly, the voltage at the right end of each ofthe res'istors"5 0 and 52. will conform to the voltage ofthelposi- .tive terminal of the transducer 22. Thus, there is a ,potential gradient fromone end'to the other of each of these resistors.

When the network 48 is inthe condition suggested by ,the[full1linesfin FIG. '4, the positive terminals of the transducers '22 and 24 will .be coupled together, and the negative terminals o'fthetransducersf22 and 24 also will be coupled together.

amplitude of the signal from the transducer 22 starts to diminish. As the contacts 54and-56 approach the mid ,points of resistors50 and 52, thebr'idge circuit composed of the transducers22.and12'4 and variable resistors 50 and I'5;2'is unbalancedinsuch a wayas to make all ofthe har- ,rnoni'csappear at the output of the circuit.

"In passing the midpoint of a resistor 50 and 52, a

phase shift also takes place. The left half of each of the resistors 50 and 52is always 'in,phase with the nega- ,tive terminal of the transducer '22, while the right half of each of the resistors 50 and T52is always in phase with the positive terminal of the transducer22.

'Whenever the contacti54jis disposed at a location betweenthe'leftendo'f the resistor. 50 and the centerof'the resistor 50,,the voltage to.be combined with the voltage from the negativeterminal of the transducer 24 will be in ,phase with the voltage from the negative terminal of the transducer '22, but it will have -lesser amplitude. 1 arly, when the contact56 occupies a position intermedi- "Simiate vthe right end of the resistor '52 .and the center of the resistor 52, thevoltage to be combined with the voltage from the, positive terminal of thetransducer 24 will :be in phase with, butof a lesser'magnitude than, the

I voltageat the positive terminal o'f'the transducer 24. The

resultjis that a partial cancellation willtake place. 'Harn1onic s which are out ofp'hase at the two transducers 22 and '24 will be partially cancelled, While the harmonics which are in phaseat the transducers 22 and 24 will pass to the amplifier 44 without any diminuation in their strength or amplitude.

The effect obtained when the contacts 54 and '56 have beenmoved past the mid pont of their respective resisters '50 and 52 is opposite in nature. In'this condition of the network 48, odd-numbered harmonics will cancel, but even-numbered harmonics will not cancel.

The degree of cancellation depends upon .the distances between the ends of the resistors 50' movable contacts-54 and 56.

Although certain embodiments of the invention .have been illustrated and described in detail, alterations and modifications will be obvious to persons of ordinary skill .It is intended therefore that the foregoing be and 52 and the consideredas exemplary only and that the scope of the invention be ascertained I claim: 1. Apparatus for producing sound comprising support means, a pair of piezoelectric transducers mounted on said from the following claims.

support means in spaced relation to each other, a vibratable string the vibrating length of which determines its vibration frequency, said string being carried by said support means and bearing against both of said transducers,

one of said transducers being located at one end of said vibrating length of said string and the other of said transducers being located at the opposite end of said vibrating length of said string, circuit means connected to said transducers for combining the electrical signals produced by said transducers when said string is vibrated, and speaker means operatively' coupled to said circuit means for convetting the resultant electrical signal into sound 2. Apparatus for producing sound comprising support means, a pair of matched piezoelectric transducers mounted on said support means in spaced relation to each other, a vibratable string the vibrating length of which determines its vibration frequency, said string being carried by said support means and bearing against both of said transducers, one of said transducers being located at one end of said vibrating length of said string and the other of said transducers being located at the opposite end of said vibrating length of said string, circuit means connected to said transducers for combining the electric signals produced by said transducers when said string is vibrated, and speaker means operatively coupled to said circuit means for converting the resultant electrical signal into sound.

3. Apparatus for producing sound comprising support means, a pair of piezoelectric transducers mounted on said support means in spaced relation to each other, a vibratable string the vibrating length of which determines its vibration frequency, said string being carried by said support means and bearing against both of said transducers, one of said transducers being located at one end of said vibrating length of said string and the other of said transducers being located at the opposite end of said vibrating length of said string, circuit means connected to said transducers for selectively combining the electrical signals produced by said transducers when said string is vibrated by selectively connecting the positive terminal of one of said transducers to either the positive or the negative terminal of the other of said transducers, and speaker means operatively coupled to said circuit means for converting the resultant electrical signal into sound.

4. Apparatus for producing sound comprising support means, a pair of piezoelectric transducers mounted on said support means in spaced relation to each other, a vibratable string the vibrating length of which determines its vibration frequency, said string being carried by said support means and bearing against both of said transducers, one of said transducers being located at one end of said vibrating length of said string and the other of said transducers being located at the opposite end of said vibrating length of said string, circuit means connected to said transducers, said circuit means including means operable selectively to uncouple said transducers or to couple the positive terminal of each transducer to the positive terminal of the other and the negative terminal of each transducer to the negative terminal of the other or to couple the positive terminal of each transducer to the negative terminal of the other, and speaker means operatively coupled to the positive and negative terminals of one of said transducers for converting the resultant electrical signal into sound.

5. Apparatus for producing sound comprising support means, first and second piezoelectric transducers mounted on said support means in spaced relation to each other, va vibratable string the vibrating length of which determines its vibration frequency, said string being carried by said support means and bearing against bo of said transducers, one of said transducers being located at one end of said vibrating length of said string and the other of said transducers being located at the opposite end of said vibrating length of said string, a resistor connected .across the positive and negative terminals of said first transducer, a contact movable along said resistor and being connected to a terminal of said second transducer, and speaker means operatively coupled to said terminal of said second transducer for converting the resultant electrical signal into sound.

6 Apparatus for producing sound comprising support means, first and second piezoelectric transducers mounted on said support means in spaced relation to each other, a vibratable string the vibrating length of which determines its vibration frequency, said string being carried by said support means and bearing against both of. said transducers, one of said transducers being located at one end of said vibrating length of said string and the other of said transducers being located at the opposite end of said vibrating length of said string, a first resistor connected across the positive and negative terminals of said first transducer, a first contact movable along said resistor and being connected to the positive terminal of said second transducer, a second resistor connected across the positive and negative terminals of said first transducer, a second contact movable along said second resistor and being connected to the negative terminal of said second transducer, and speaker means operativcly coupled to said terminals of said second transducer for converting the re sultant electrical signal into sound.

7. Apparatus for producing sound comprising support means, first and second piezoelectric transducers mounted on said support means in spaced relation to each other, a vibratable string the vibrating length of which determines its vibration frequency, said string being carried by said support means and bearing against both of said transducers, one of said transducers being located at one end of said vibrating length of said string and the other of said transducers being located at the opposite end of said vibrating length of said string, a first resistor connected across the positive and negative terminals of said first transducer, a first contact movable along said resistor and being connected to the positive terminal of said second transducer, a second resistor connected across the positive and negative terminals of said first transducer, a second contact movable along said second resistor and being connected to the negative terminal of said second transducer, means mechanically connecting said first and second contacts together for simultaneous movement in opposite directions along said resistors, and speaker means operatively coupled to said terminals of said second transducer for converting the resultant electrical signal into sound.

References Cited in the file of this patent UNITED STATES PATENTS 890,803 Severy et al. June 16, 1908 1,693,806 Cady Dec. 4, 1928 1,961,410 Wegel June 5, 1934 2,148,478 Kock Feb. 28, 1939 2,484,950 Iaife Oct. 18, 1949 2,494,485 Notara Jan. 10, 1950 2,769,867 Crownover Nov. 6, 1956 2,817,261 Fender Dec. 24, 1957 2,944,117 Gray July 5, 1960 

1. APPARATUS FOR PRODUCING SOUND COMPRISING SUPPORT MEANS, A PAIR OF PIEZOELECTRIC TRANSDUCERS MOUNTED ON SAID SUPPORT MEANS IN SPACED RELATION TO EACH OTHER, A VIBRATABLE STRING THE VIBRATING LENGTH OF WHICH DETERMINES ITS VIBRATION FREQUENCY, SAID STRING BEING CARRIED BY SAID SUPPORT MEANS AND BEARING AGAINST BOTH OF SAID TRANSDUCERS, ONE OF SAID TRANSDUCERS BEING LOCATED AT ONE END OF SAID VIBRATING LENGTH OF SAID STRING AND THE OTHER OF SAID TRANSDUCERS BEING LOCATED AT THE OPPOSITE END OF SAID VIBRATING LENGTH OF SAID STRING, CIRCUIT MEANS CONNECTED TO SAID TRANSDUCERS FOR COMBINING THE ELECTRICAL SIGNALS PRODUCED BY SAID TRANSDUCERS WHEN SAID STRING IS VIBRATED, AND SPEAKER MEANS OPERATIVELY COUPLED TO SAID CIRCUIT MEANS FOR CONVERTING THE RESULTANT ELECTRICAL SIGNAL INTO SOUND. 